Centripetal Force

Example: A centrifuge has a rotational speed of 11,000 rpm.

a. What is the centripetal acceleration (a_{c}) of a molecule situated a distance of 6 cm from the axis of rotation?

b. How does the acceleration from part a (a_{c}) compare with the acceleration due to gravity?


  • w=11,000\ rpm
  • r=6\ cm


  • v_{t}=\ ?
  • a_{c}=\ ?

Draw a picture:











Convert units to standard form:

w=11.000\ \frac{rotation}{min}\times\frac{1\ min}{60\ sec}\times\frac{2\pi\ radian}{rotation}=1152\ \frac{rad}{s}=w

r=0.06\ m

Solve for velocity (speed):

v_{t}=w\times r

1152\ \frac{rad}{s}\times 0.06\ m=69.12\ \frac{m}{s}

Solve for acceleration (a_{c}):

a_{c}=\frac{v_{t}^{2}}{r}=\frac{(69.12\ \frac{m}{s})^{2}}{0.06\ m}=79,615\ \frac{m}{s^2}

Compare to gravity:

g=9.81\ \frac{m}{s^2}

a_{c}=79,615\ \frac{m}{s^2}

\frac{a_{c}}{g}\Rightarrow a_{c}=8115\ times\ larger\ than\ g